Rotational entropy is related to the number of distinct ways the particles can be arranged in the same structure. The greater the number of arrangements, the greater the entropy. There are exactly 720 possible ways six particles can be arranged into the highly symmetrical octahedron, and also 720 for the asymmetrical poly-tetrahedron. But there is redundancy within these numbers. In some cases different arrangements are revealed to be the same when the structure is rotated about an axis of symmetry. To get a true number of possible permutations to find the true rotational entropy, all arrangements that are the same when rotated should be counted as a single arrangement.